Question

The first ionization energy of na(g) is 0.50 mj/mole. can a photon with a wavelength of 500 nm ionize a sodium atom? explain.

Answer 1

No, a photon with a wavelength of 500 nm cannot ionize a sodium atom. This is because energy of the photon is less than the energy required to ionize a single gaseous sodium atom.

Step-by-step explanation:

The first ionization energy of Na(g) is 0.50 MJ/mole =
`5* 10^5 J/mol`

1 Mega Joule =
`10^6 J`

The first ionization energy of 1 Na(g) atom =
`E_s=(5* 10^5 J/mol)/(6.022* 10^(23) mol^(-1))=8.3028* 10^(-19) J`

If we have a photon of wavelength = 500 nm =
`5.00* 10^(-7) m`

`1 nm = 10^(-9) m`

`E=(h* c)/(\lambda)`

E = energy of photon = ?

`\lambda` = wavelength

h = Planck's constant =
`6.63* 10^(-34)Js`

c = speed of light =
`3* 10^8m/s`

`E=(6.63* 10^(-34)J s* 3* 10^8 m/s)/(5.00* 10^(-7)m)=3.978* 10^(-19) J`

Energy of the photon = E =
`3.978* 10^(-19) J`

As we can see that ,
`E_s>E`

Photon of this wavelength will not able to ionize the sodium atom.This is because energy of the photon is less than the energy required to ionize a single gaseous sodium atom.

A photon with a wavelength of 500 nm cannot ionize a sodium atom.

Answer 2

No, a photon with a wavelength of 500 nm can't ionize a sodium atom.

Step-by-step explanation:

Step 1: Find out Energy of given wavelength:

The relation between wavelength and frequency is as follow,

υ = c / λ

where

υ = frequency = ?

c = velocity of light = 3.0 × 10⁸ ms⁻¹

λ = wavenumber = 500 nm = 500 × 10⁻⁹ m

Putting the given values,

υ = 3.0 × 10⁸ ms⁻¹ / 500 × 10⁻⁹ m

υ = 6.0 × 10¹⁴ s⁻¹

Also we know that,

E = h υ

Where;

E = Energy

h = Plank's Constant = 6.6262 × 10⁻³⁴ Js

Putting value of frequency,

E = 6.6262 × 10⁻³⁴ Js × 6.0 × 10¹⁴ s⁻¹

E = 3.97 × 10⁻¹⁹ J

Step 2: Compare given energy and calculated energy:

As we know,

0.5 mJ = 500000 J

Also,

500000 J > 3.97 × 10⁻¹⁹ J

Conclusion:

The energy of calculated wavelength of photon is less than 0.5 mJ hence, it is unable to ionize sodium atom.